Basic properties
| Modulus: | \(1350\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(383,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1350.bi
\(\chi_{1350}(23,\cdot)\) \(\chi_{1350}(47,\cdot)\) \(\chi_{1350}(77,\cdot)\) \(\chi_{1350}(83,\cdot)\) \(\chi_{1350}(113,\cdot)\) \(\chi_{1350}(137,\cdot)\) \(\chi_{1350}(167,\cdot)\) \(\chi_{1350}(173,\cdot)\) \(\chi_{1350}(203,\cdot)\) \(\chi_{1350}(227,\cdot)\) \(\chi_{1350}(263,\cdot)\) \(\chi_{1350}(317,\cdot)\) \(\chi_{1350}(347,\cdot)\) \(\chi_{1350}(353,\cdot)\) \(\chi_{1350}(383,\cdot)\) \(\chi_{1350}(437,\cdot)\) \(\chi_{1350}(473,\cdot)\) \(\chi_{1350}(497,\cdot)\) \(\chi_{1350}(527,\cdot)\) \(\chi_{1350}(533,\cdot)\) \(\chi_{1350}(563,\cdot)\) \(\chi_{1350}(587,\cdot)\) \(\chi_{1350}(617,\cdot)\) \(\chi_{1350}(623,\cdot)\) \(\chi_{1350}(653,\cdot)\) \(\chi_{1350}(677,\cdot)\) \(\chi_{1350}(713,\cdot)\) \(\chi_{1350}(767,\cdot)\) \(\chi_{1350}(797,\cdot)\) \(\chi_{1350}(803,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1001,1027)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{3}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 1350 }(383, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{13}{180}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{29}{90}\right)\) |